The mean proportion of $$\frac{a^2}{b^3}$$​ and  $$\frac{9b^2}{4a^3}$$​ is _______.

Correct option is B

Given:

-Two quantities: $$\frac{a^2}{b^3}\ and\ \frac{9b^2}{4a^3}$$​​

Formula Used:

- Mean proportion between two numbers x and y is given by: √(x × y)

Solution:

Mean proportion 

​$$\sqrt{\left(\frac{a^2}{b^3} \times \frac{9b^2}{4a^3}\right)} \\\ \\= \sqrt{\left(\frac{a^2 \cdot 9b^2}{b^3 \cdot 4a^3}\right)} \\\ \\= \sqrt{\left(\frac{9a^2b^2}{4a^3b^3}\right)} \\\ \\= \sqrt{\left(\frac{9}{4} \cdot \frac{1}{ab}\right)} \\\ \\= \frac{3}{2} \cdot \frac{1}{\sqrt{ab}} \\\ \\= \frac{3}{2\sqrt{ab}}$$​​